The routine reduces the target of M by elementary moves (see elementary) involving just d+1 variables. The outcome is probabalistic, but if the routine fails, it gives an error message.
i1 : kk=ZZ/32003 o1 = kk o1 : QuotientRing |
i2 : S=kk[a..e] o2 = S o2 : PolynomialRing |
i3 : i=ideal(a^2,b^3,c^4, d^5) 2 3 4 5 o3 = ideal (a , b , c , d ) o3 : Ideal of S |
i4 : F=res i 1 4 6 4 1 o4 = S <-- S <-- S <-- S <-- S <-- 0 0 1 2 3 4 5 o4 : ChainComplex |
i5 : f=F.dd_3 o5 = {5} | c4 d5 0 0 | {6} | -b3 0 d5 0 | {7} | a2 0 0 d5 | {7} | 0 -b3 -c4 0 | {8} | 0 a2 0 -c4 | {9} | 0 0 a2 b3 | 6 4 o5 : Matrix S <--- S |
i6 : EG = evansGriffith(f,2) -- notice that we have a matrix with one less row, as described in elementary, and the target module rank is one less. o6 = {5} | c4 d5 0 {6} | -b3 0 d5 {7} | 0 -b3 3928a4-7203a3b+8639a2b2+10242a3c+7586a2bc+3748a2c2-c4 {7} | a2 0 -8231a4-3836a3b-916a2b2+1971a3c+10179a2bc-4410a2c2 {8} | 0 a2 -2718a3-12547a2b-8242a2c ------------------------------------------------------------------------ 0 | 0 | 3928a2b3-7203ab4+8639b5+10242ab3c+7586b4c+3748b3c2 | -8231a2b3-3836ab4-916b5+1971ab3c+10179b4c-4410b3c2+d5 | -2718ab3-12547b4-8242b3c-c4 | 5 4 o6 : Matrix S <--- S |
i7 : isSyzygy(coker EG,2) o7 = true |